List of series

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This list of mathematical series contains formulae for finite and infinite sums. It can be used in conjunction with other tools for evaluating sums.

Sums of powers[change | change source]

  • See also triangle number. This is one of the most useful series: many applications can be found throughout mathematics.
  • Where is the th Bernoulli number, is negative and is the binomial coefficient (choose function).
Where is the Riemann zeta function.

Power series[change | change source]

Infinite sum (for ) Finite sum
where and
where Lis(x) is the polylogarithm of x.

Simple denominators[change | change source]

Factorial denominators[change | change source]

Many power series which arise from Taylor's theorem have a coefficient containing a factorial.

  • (c.f. mean of Poisson distribution)
  • (c.f. second moment of Poisson distribution)

Modified-factorial denominators[change | change source]

Binomial series[change | change source]

Geometric series:

Binomial Theorem:

with generalized binomial coefficients

Square root:


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  • [1]
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Binomial coefficients[change | change source]

Trigonometric functions[change | change source]

Sums of sines and cosines arise in Fourier series.

Unclassified[change | change source]

Related pages[change | change source]

Notes[change | change source]

  1. 1.0 1.1 1.2 1.3 Theoretical computer science cheat sheet

References[change | change source]